Solve {l}{0.8div40.2}{-0.9*[-10.2-(11.1)]div[-0.2+(-0.1)]}

$$\left. \begin{array} { l } { 0.8 \div 40.2 } \\ { - 0.9 \times [ - 10.2 - ( 11.1 ) ] \div [ - 0.2 + ( - 0.1 ) ] } \end{array} \right.$$

Evaluate

$$-\frac{128399}{2010}\approx -63.880099502$$

Solution Steps

Expand \frac{0.8}{40.2} by multiplying both numerator and the denominator by 10.

$$\frac{8}{402}-\frac{0.9\left(-10.2-11.1\right)}{-0.2-0.1}$$

Reduce the fraction \frac{8}{402} to lowest terms by extracting and canceling out 2.

$$\frac{4}{201}-\frac{0.9\left(-10.2-11.1\right)}{-0.2-0.1}$$

Subtract 11.1 from -10.2 to get -21.3.

$$\frac{4}{201}-\frac{0.9\left(-21.3\right)}{-0.2-0.1}$$

Multiply 0.9 and -21.3 to get -19.17.

$$\frac{4}{201}-\frac{-19.17}{-0.2-0.1}$$

Subtract 0.1 from -0.2 to get -0.3.

$$\frac{4}{201}-\frac{-19.17}{-0.3}$$

Expand \frac{-19.17}{-0.3} by multiplying both numerator and the denominator by 100.

$$\frac{4}{201}-\frac{-1917}{-30}$$

Reduce the fraction \frac{-1917}{-30} to lowest terms by extracting and canceling out -3.

$$\frac{4}{201}-\frac{639}{10}$$

Least common multiple of 201 and 10 is 2010. Convert \frac{4}{201} and \frac{639}{10} to fractions with denominator 2010.

$$\frac{40}{2010}-\frac{128439}{2010}$$

Since \frac{40}{2010} and \frac{128439}{2010} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-128439}{2010}$$

Subtract 128439 from 40 to get -128399.

$$-\frac{128399}{2010}$$

Factor

$$-\frac{128399}{2010} = -63\frac{1769}{2010} = -63.88009950248756$$